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exp-Gravity2D.lisp
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exp-Gravity2D.lisp
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;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
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;;;
;; @file exp-Gravity2D.lisp
;; @author Mitch Richling <https://www.mitchr.me>
;; @brief Demonstrate the danger of assuming everything is a sphere in gravity problems.@EOL
;; @std Common Lisp
;; @copyright
;; @parblock
;; Copyright (c) 2015, Mitchell Jay Richling <https://www.mitchr.me> All rights reserved.
;;
;; Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
;;
;; 1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
;;
;; 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
;; and/or other materials provided with the distribution.
;;
;; 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
;; without specific prior written permission.
;;
;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
;; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
;; LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
;; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
;; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
;; DAMAGE.
;; @endparblock
;; @filedetails
;;
;; We compare two scenarios:
;;
;; Three Iridium spheres. One (m1) of radius 1000m located at (0, 2000), a second (m2) of the same radius located at (0, -2000), and a third (mp) of radius
;; 10 who's location varies from (1000*2^(1/3)+10, 0) to (10000, 0). We compute the magnitude of the gravitational force on the small sphere assuming the
;; large spheres stay fixed.
;;
;; Two Iridium spheres. One (m0) with radius 1000*2^(1/3) (twice the mass of each big sphere in the previous scenario), and a second sphere (mp) of radius
;; 10 who's location varies from (1000*2^(1/3)+10, 0) to (10000,0). We compute the magnitude of the gravitational force on the small sphere assuming the
;; large sphere stays fixed.
;;
;; The total mass in both systems is the same. The larger sphere in the second scenario is located at the center of mass for the two large spheres in the
;; first scenario. One might be tempted to combine the two large spheres into a single sphere located at the center of mass when faced with this problem;
;; however, this experiment shows the very different forces involved.
;;
;; Note: I used my vec_ package, but this is a 2D problem that could have been done with complex numbers...
;;
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(flet ((mi (r) (* (expt r 3) pi 4/3 22560))) ;; Compute the mass of an Iridium sphere of given radius
(let* ((p (vector 0 0))
(b0 (vector 0 0))
(b1 (vector 0 2000))
(b2 (vector 0 -2000))
(G 6.67428L-11)
(r1 1000)
(m1 (mi r1))
(r2 1000)
(m2 (mi r2))
(r0 (* r1 (expt 2 1/3)))
(m0 (mi r0))
(rp 10)
(mp (mi rp))
(dat (mjr_dquad_make-from-axis "x" (list :start (+ r0 rp) :end (* 10 (+ r0 rp)) :len 100))))
(mjr_dquad_add-data-from-map dat
(lambda (x)
(setf (aref p 0) x)
(mjr_vec_norm-two
(mjr_vec_+ (mjr_vec_/ (mjr_vec_* (mjr_vec_- p b1) (* G m1 mp)) (mjr_vec_norm-two-squared (mjr_vec_- p b1)))
(mjr_vec_/ (mjr_vec_* (mjr_vec_- p b2) (* G m2 mp)) (mjr_vec_norm-two-squared (mjr_vec_- p b2))))))
:axes 't
:ano-nam "dfv"
:ano-typ :ano-typ-real)
(mjr_dquad_add-data-from-map dat
(lambda (x)
(setf (aref p 0) x)
(mjr_vec_norm-two (mjr_vec_/ (mjr_vec_* (mjr_vec_- p b0) (* G m0 mp)) (mjr_vec_norm-two-squared (mjr_vec_- p b0)))))
:axes 't
:ano-nam "sfv"
:ano-typ :ano-typ-real)
(mjr_gnupl_dquad dat :xlab "distance" :ylab "force" :main "Difference between two gravity sources and a single one")))